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We consider the application of the original Meyer-Miller (MM) Hamiltonian tomapping fermionic quantum dynamics to classical equations of motion.Non-interacting fermionic and bosonic systems share the same one-body densitydynamics when evolving from the same initial many-body state. The MM classicalmapping is exact for non-interacting bosons, and therefore it yields the exacttime-dependent one-body density for non-interacting fermions as well. Startingfrom this observation, the MM mapping is compared to different mappingsspecific for fermionic systems, namely the spin mapping (SM) with and withoutincluding a Jordan-Wigner transformation, and the Li-Miller mapping (LMM). Fornon-interacting systems, the inclusion of fermionic anti-symmetry through theJordan-Wigner transform does not lead to any improvement in the performance ofthe mappings and instead it worsens the classical description. For aninteracting impurity model and for models of excitonic energy transfer, the MMand LMM mappings perform similarly, and in some cases the former outperformsthe latter when compared to a full quantum description. The classical mappingsare able to capture interference effects, both constructive and destructive,that originate from equivalent energy transfer pathways in the models.

A bosonic perspective on the classical mapping of fermionic quantum dynamics